Question

a, b are the roots of ax? +bx+c=0, then find the equation whose roots are 2+a , 2+ ß​

Answer 1

$\huge\mathfrak\color {red}ANSWER$

α,β are the roots of ⇒ax2+bx+c=0

Then, a(α)2+b(α)+c=0

Now, α+2=x

Hence, α=x−2

Thus, replace α by x−2 in the given equation,

Required equation is

a(x−2)2+b(x−2)+c=0

⇒a(x2−4x+4)+bx−2b+c=0

⇒ax2+(b−4a)x+(4a−2b+c)=0

⇒ax2+x(b−4a)+4a−2b+c=0